1
WB JEE 2020
+1
-0.25
The unit vector in ZOX plane, making angles $$45^\circ$$ and $$60^\circ$$ respectively with $$\alpha = 2\widehat i + 2\widehat j - \widehat k$$ and $$\beta = \widehat j - \widehat k$$ is
A
$${1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat j$$
B
$${1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat k$$
C
$${1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat j$$
D
$${1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat k$$
2
WB JEE 2019
+2
-0.5
Let $$\widehat \alpha$$, $$\widehat \beta$$, $$\widehat \gamma$$ be three unit vectors such that $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )$$ where $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) =$$$$(\widehat \alpha \,.\,\widehat \gamma )\widehat \beta - (\widehat \alpha \,.\,\widehat \beta )\widehat \gamma$$. If $$\widehat \beta$$ is not parallel to $$\widehat \gamma$$, then the angle between $$\widehat \alpha$$ and $$\widehat \beta$$ is
A
$${{5\pi } \over 6}$$
B
$${{\pi } \over 6}$$
C
$${{\pi } \over 3}$$
D
$${{2\pi } \over 3}$$
3
WB JEE 2019
+2
-0.5
The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\widehat j + 2\widehat k$$, $$5\widehat i - \widehat j + 2\widehat k$$ and $$4\widehat i - \widehat j - \lambda \widehat k$$, respectively. If the points A, B, C and D lie on a plane, the value of $$\lambda$$ is
A
0
B
1
C
2
D
$$-$$ 4
4
WB JEE 2018
+2
-0.5
Let $$\overrightarrow \alpha$$ = $$\widehat i + \widehat j + \widehat k$$, $$\overrightarrow \beta$$ = $$\widehat i - \widehat j - \widehat k$$ and $${\overrightarrow \gamma }$$ = $$- \widehat i - \widehat j - \widehat k$$ be three vectors. A vector $$\overrightarrow \delta$$, in the plane of $$\overrightarrow \alpha$$ and $$\overrightarrow \beta$$, whose projection on $${\overrightarrow \gamma }$$ is $${1 \over {\sqrt 3 }}$$, is given by
A
$$- \widehat i - 3\widehat j - 3\widehat k$$
B
$$\widehat i - 3\widehat j - 3\widehat k$$
C
$$- \widehat i + 3\widehat j + 3\widehat k$$
D
$$\widehat i + 3\widehat j - 3\widehat k$$
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